How do you solve #abs(x-20<4#?

1 Answer
May 31, 2015

Alternative Version of Question 1
#abs(x) - 20 <4#
#color(white)("XXXXX")##abs(x) < 24#
#color(white)("XXXXX")##rarr -24 < x < 24#

Alternate Version of Question 2
#abs(x-20) <4#
#color(white)("XXXXX")#Case 1: #(x-20)<0 rarr x < 20#
#color(white)("XXXXX")##color(white)("XXXXX")##abs(x-20) < 4#
#color(white)("XXXXX")##color(white)("XXXXX")##20-x < 4#
#color(white)("XXXXX")##color(white)("XXXXX")##x > 16#
#color(white)("XXXXX")##16 < x < 20#

#color(white)("XXXXX")#Case2: #(x-20)>=0 rarr x>= 20#
#color(white)("XXXXX")##color(white)("XXXXX")##abs(x-20) < 4#
#color(white)("XXXXX")##color(white)("XXXXX")##x-20 < 4#
#color(white)("XXXXX")##color(white)("XXXXX")##x < 24#
#color(white)("XXXXX")##20 <= x < 24#

Combining Case 1 and Case 2
#color(white)("XXXXX")##16 < x < 24#